A Type Of Optimal Consumption And Investment Model Study

The problem of optimal consumption-investment refers to the agent's capital being distributed between consumption and portfolio,expecting maximum utility from terminal wealth and/or intermediate consumption over[0,T]or[0,∞).In this paper,we mainly study the problem of optimal consumption and portfolio with transaction costs,random income,and with consumption constraints, stopping,respectively.This paper is divided into three chapters.In chapter 1, first we introduce the history of optimal problem about consumption-investment in continuous-time,then we put forward the problem that we study in this thesis,last we introduce some prepare knowledge about optimal consumption and portfolio in a continuous-time.Chapter 2 assume that there are market frictions.In the presence of transaction fee,the martingale and duality methodology are used for studying the optimal consumption-investment with random income.By introducing an auxiliary optimization problem which is "dual" to the "primal" utility maximization question, we analysis the relation between the primal and dual problems,and explain how a solution to the latter induces one for the former.In chapter 3,in the complete financial market model,we study an optimal consumption-investment with minimal consumption constraints and stopping.Simplify the initial optimization problem by introducing the modified utility function corresponding the consumption constraints. The martingale and convex duality theory are employed for obtaining the optimal solution of problem and sufficient conditions for the existence of optimal strategies.